(adjective) free from guilt; harmless; artless; (noun) dimwit
The modern senses are the oldest ones, known in English from the 14th century and often found in Shakespeare. Hero, for example, is often described as "innocent" in Act V of Much Ado About Nothing. But during the 16th century a negative sense developed, so that people described as "innocent" (either as adjective or noun) were held to be half-witted simpletons. It is this sense of "silly, foolish" which we must look out for in the plays. It appears very clearly when the Gaoler describes the way his daughter answered his questions "as if she were a fool, An innocent" (The Two Noble Kinsmen, IV.i.41). Parolles also describes Dumaine being whipped "for getting the shrieve's fool with child, a dumb innocent" (All's Well That Ends Well, IV.iii.184). There is just one example of the adjectival use in this sense, when Benedick reflects on his poetic abilities (Much Ado About Nothing, V.ii.37): "I can find out no rhyme to 'lady' but 'baby' - an innocent rhyme". He doesn't mean that the rhyme has no wicked meaning: it's a bad rhyme, worthy of a half-wit.